Why is the taylor series for ln(x+1) so similar to the tailor series sin(x) or cos(x), yet the functions themselves are not at all?

Question

Why is the taylor series for ln(x+1) so similar to the tailor series sin(x) or cos(x), yet the functions themselves are not at all?

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Answer 1

I’m a bit confused, they aren’t the same at all. The taylor series terms for ln(x+1) are x^n / n alternating signs.

The taylor series for sin(x) has terms x^2n+1 / (2n+1)! (alternating signs).

The taylor series for sin(x) has terms x^2n / (2n)! (alternating signs).

These are very different.